2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50507A kind of Dirac-Connes operator defined in the framework of Connes' NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, Müller-Hoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices.Latex, 9 pages, no figures; References addedHigh Energy Physics - TheoryHigh Energy Physics - LatticeMathematical PhysicsDirac-Connes Operator on Discrete Abelian Groups and Latticestext